About Finish Line Mathematics 5

Transcription

1 Table of COntents About Finish Line Mathematics 5 Unit 1: Big Ideas from Grade 4 7 Lesson 1 4.NBT.5, 6 Multiplying and Dividing Whole Numbers [connects to 5.NBT.5, 6] 8 Lesson 2 4.NF.6, 7 Understanding Decimals [connects to 5.NBT.3.a, b] 15 Lesson 3 4.NF.3.a, c, d Adding and Subtracting Fractions [connects to 5.NF.1, 2, 6] 23 Lesson 4 4.MD.1 Finding Equivalent Measurements [connects to 5.MD.1] 30 Unit 1 Review 38 Unit 2: Number and Operations in Base Ten 42 Lesson 5 5.NBT.1 Whole-Number Place Value 43 Lesson 6 5.NBT.2 Powers of Ten 50 Lesson 7 5.NBT.1, 3.a Decimal Names and Place Value 57 Lesson 8 5.NBT.3.b Comparing Decimals 64 Lesson 9 5.NBT.4 Rounding Decimals 71 Lesson 10 5.NBT.5 Multiplying Whole Numbers 78 Lesson 11 5.NBT.6 Dividing Whole Numbers 85 Lesson 12 5.NBT.7 Adding and Subtracting Decimals 92 Lesson 13 5.NBT.7 Multiplying Decimals 99 Lesson 14 5.NBT.7 Dividing Decimals 107 Unit 2 Review 116 Unit 3: Operations and Algebraic Thinking 120 Lesson 15 5.OA.1, 2 Understanding and Writing Expressions 121 Lesson 16 5.OA.1 Evaluating Expressions 128 Lesson 17 5.OA.3 Patterns and Relationships 135 Unit 3 Review 144

2 Unit 4: Number and Operations Fractions 149 Lesson 18 5.NF.1 Adding and Subtracting Fractions with Unlike Denominators 150 Lesson 19 5.NF.2 Word Problems with Addition and Subtraction of Fractions 158 Lesson 20 5.NF.3 Connecting Fractions and Division 165 Lesson 21 5.NF.4.a, b Multiplying Whole Numbers and Fractions 172 Lesson 22 5.NF.4.a, b Multiplying Fractions 178 Lesson 23 5.NF.5.a, b Multiplication and Scale 185 Lesson 24 5.NF.6 Word Problems with Multiplication of Fractions 192 Lesson 25 5.NF.7.a, b Dividing with Unit Fractions 199 Lesson 26 5.NF.7.c Word Problems with Division and Fractions 206 Unit 4 Review 213 Unit 5: Measurement and Data 218 Lesson 27 5.MD.1 Measurement Conversions 219 Lesson 28 5.MD.2 Measurement Data on Line Plots MD.3.a, b; 4 Understanding Volume 237 Lesson 30 5.MD.5.a, b Volume of Rectangular Prisms 244 Lesson 31 5.MD.5.c Volume of Irregular Figures 252 Unit 5 Review 260 Unit 6: Geometry 265 Lesson 32 5.G.1 Using the Coordinate Plane 266 Lesson 33 5.G.2 Solving Problems with the Coordinate Plane 274 Lesson 34 5.G.3 Properties of Two-Dimensional Figures 282 Lesson 35 5.G.4 Classifying Two-Dimensional Figures 291 Unit 6 Review 300 Glossary 305 Flash Cards 313

3 LessoN 29 Understanding Volume CCSS: 5.MD.3.a, b; 4 PART 1 Introduction Volume is a measure of the amount of space an object takes up. It can be measured by finding the number of cubic units it takes to fill the object without overlapping and without spaces between the units. A cubic unit is the volume of a cube that has a side length of 1 unit. This type of cube is known as a unit cube. It is 1 unit wide, 1 unit long, and 1 unit tall. 1 unit 1 unit 1 unit A cube with side lengths measuring 1 unit has a volume of 1 cubic unit, or 1 unit 3. A cube is a rectangular prism with sides of equal length. A small box that is 2 inches wide, 2 inches long, and 6 inches tall arrives in the mail. What is the volume of the box in cubic inches? To find the volume of the box, you can stack unit cubes inside the box. Think of making layers of cubes. One layer has 2 rows of 2 cubes. So there are 4 cubes in a layer. One layer is 4 cubic inches. 1 in. The side length of the unit cube can be measured in any unit of length. A side length of 1 centimeter means the volume is 1 cubic centimeter (cm 3 ). 1 in. 1 in. The box is 6 inches high. So it has 6 layers like the one above. There are 24 cubes in the entire box, so the volume is 24 cubic inches. Cubic inches can be written as cubic inches or in. 3. Think About It Why might it be important to be able to measure the volume of a box used to ship a package? UNIT 5 Measurement and Data 237

4 2 Focused Instruction Work with a partner to build a model using unit cubes to help you understand this volume problem. Ansel s dad ordered a new chair. The chair was delivered in a box that measured 6 feet long, 3 feet wide, and 5 feet tall. What is the volume of the box? 5 ft 6 ft 3 ft Build a model of the box using unit cubes. First, make a row of unit cubes. How many cubes will be in a row? Think of the row as the length of the box. How many rows of unit cubes are in each layer? How many unit cubes are in each layer? How many layers of cubes are in the model? How high is the box? Since each layer has the same number of cubes in it, what operation can you use to find the number of cubes in the total number of layers? Multiply the number of layers by the number of unit cubes in each layer. How many unit cubes are there in all? What is the volume of the box? Each unit cube has a volume of 1 cubic foot (1 ft 3 ). 238 UNIT 5 Measurement and Data

5 2 Focused Instruction Count the cubes that make up a rectangular prism to find the volume. You will not be able to see all the cubes. The rectangular prism below is made up of cubes measuring 1 yard on each edge. Can you see all the cubes in the figure? How can you tell how many cubes are in the figure? How can you tell what cubes are hidden behind others? What is the volume of each unit cube? How many unit cubes are in the bottom layer of the prism? How many layers are in the model? Multiply the number of layers by the number of unit cubes in each layer. How many unit cubes are there in all? What is the volume of the rectangular prism? Use what you know about volume to find the volume of these objects. 1 2 UNIT 5 Measurement and Data 239

6 3 Guided Practice Solve the following problems. 1 A closet is 5 feet wide, 4 feet long, and 7 feet tall. Explain how to find the volume of the closet using boxes that measure 1 foot on each edge. Think of the closet in layers. What is the volume of one layer? 2 A rectangular figure has one layer filled with the cubes shown. If the figure is 4 units tall, how many layers like the model shown will the figure have? If the figure is 4 units tall, write an expression that can be used to find the volume of the figure. Answer 3 Luca is packing a truck s cargo section with boxes. Each box is 1 cubic yard. If the truck s cargo section is 2 yards wide by 2 yards high by 5 yards deep, how many boxes can fit? 2 yd 5 yd 2 yd Count the number of boxes measuring 1 cubic yard that can be stacked in each layer. Answer boxes 240 UNIT 5 Measurement and Data

7 4 Independent Practice Solve the following problems. 1 Which of these rectangular prisms have a volume of 30 cubic units? Select the three correct answers. A B C D E F 2 A rectangular prism that is 1 centimeter high has a volume of 56 cubic centimeters. If the prism is made up of 7 rows of 1-cubic-centimeter cubes, how many cubes are in each row? Answer cubes UNIT 5 Measurement and Data 241

8 4 Independent Practice 3 Draw a model that can be used to find the volume of a figure with a length of 8 feet, a width of 1 foot, and a height of 3 feet. 4 Cassandra buys a wireless speaker like the one shown. 4 in. 9 in. 4 in. Draw a model with unit cubes that can be used to find the volume of the speaker. 242 UNIT 5 Measurement and Data

9 4 Independent Practice 5 Giles is filling a rectangular swimming pool with water. A side of the pool is 20 feet long, another side is 10 feet long, and the depth of the pool is 4 feet. 4 ft 20 ft 10 ft Explain how Giles can find the volume of the pool using a model and cubic units. 6 Faith had 16 crates that measure 1 cubic foot each. She stacked them to form a rectangular prism. Part A What was the volume of the prism Faith made with all the crates? Answer cubic feet Part B Explain whether or not the figure below has the same volume as Faith s prism. 1 cubic inch UNIT 5 Measurement and Data 243